>Bbb23: revert sock

2025-02-26T02:17:02Z

revert sock

New page

{{Redirect|6,000|the Jewish year|Year 6000|other uses|6000 (disambiguation)}}
{{Refimprove|date=December 2009}}
{{Infobox number
| number = 6000
|ordinal text=
| roman = {{Overline|V}}M, or {{Overline|VI}}
| unicode = {{Overline|V}}M, {{Overline|v}}m, {{Overline|VI}}, {{Overline|vi}}
|lang1=[[Armenian numerals|Armenian]]|lang1 symbol=Ց}}

'''6000''' ('''six thousand''') is the [[natural number]] following 5999 and preceding 6001.

==Selected numbers in the range 6001–6999==

===6001 to 6099===
* '''6025''' – Stage name of rhythm guitarist of the [[Dead Kennedys]] from June 1978 to March 1979. Full name is [[Carlos Cadona]].
* '''6028''' – [[centered heptagonal number]]<ref name=A069099>{{cite OEIS|A069099|Centered heptagonal numbers.}}</ref>
* '''6037''' – [[super-prime]], prime of the form 2p-1
* '''6042''' – [[6042 Cheshirecat]] is a [[Mars-crossing asteroid]].
* '''6047''' – [[safe prime]]
* '''6053''' – [[Sophie Germain prime]]
* '''6069''' – [[nonagonal number]]<ref name=A001106>{{cite OEIS|A001106|2=9-gonal (or enneagonal or nonagonal) numbers: a(n) = n*(7*n-5)/2.}}</ref>
* '''6073''' – [[balanced prime]]
* '''6079''' – The serial number Winston Smith is referred to as in the [[George Orwell]] novel ''[[Nineteen Eighty-Four]]''
* '''6084''' = 782, sum of the cubes of the first twelve integers
* '''6081''' - sum of the first 54 primes
* '''6089''' – [[highly cototient number]]<ref>{{cite OEIS|A100827|Highly cototient numbers: records for a(n) in A063741.}}</ref>
* '''6095''' – [[magic constant]] of ''n'' × ''n'' normal [[magic square]] and [[Eight queens puzzle|n-Queens Problem]] for ''n'' = 23.

===6100 to 6199===
* '''6101''' – Sophie Germain prime
* '''6105''' – [[triangular number]]
* '''6113''' – Sophie Germain prime, [[super-prime]]
* '''6121''' – prime of the form 2p-1
* '''6131''' – Sophie Germain prime, [[twin prime]] with 6133
* '''6133''' – 800th prime number, twin prime with 6131
* '''6143''' – [[Thabit number]]
* '''6144''' – [[3-smooth]] number (211×3)
* '''6173''' – Sophie Germain prime
* '''[[6174 (number)|6174]]''' – Kaprekar's constant
* '''6181''' – [[octahedral number]]<ref>{{cite OEIS|A005900|2=Octahedral numbers: a(n) = n*(2*n^2 + 1)/3.}}</ref>

===6200 to 6299===
* '''6200''' – [[harmonic divisor number]]<ref>{{cite OEIS|A001599|Harmonic or Ore numbers: numbers k such that the harmonic mean of the divisors of k is an integer.}}</ref>
* '''6201''' – [[square pyramidal number]]<ref name=A000330>{{cite OEIS|A000330|2=Square pyramidal numbers: a(n) = 0^2 + 1^2 + 2^2 + ... + n^2 = n*(n+1)*(2*n+1)/6.}}</ref>
* '''6216''' – triangular number
* '''6217''' – [[super-prime]], prime of the form 2p-1
* '''6229''' – [[super-prime]]
* '''6232''' – [[amicable number]] with 6368
* '''{{vanchor|6236}}''' – Most widely accepted figure for the number of verses in the [[Qur'an]]{{citation needed|date=June 2014}}
* '''6241''' = 792, [[centered octagonal number]]<ref name=A016754>{{cite OEIS|A016754|2=Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers.}}</ref>
* '''6250''' – [[Leyland number]]<ref>{{cite OEIS|A076980|2=Leyland numbers: 3, together with numbers expressible as n^k + k^n nontrivially, i.e., n,k > 1 (to avoid n = (n-1)^1 + 1^(n-1)).}}</ref>
* '''6263''' – Sophie Germain prime, balanced prime
* '''6269''' – Sophie Germain prime
* '''6280''' – [[decagonal number]]<ref name=A001107>{{cite OEIS|A001107|2=10-gonal (or decagonal) numbers: a(n) = n*(4*n-3).}}</ref>

===6300 to 6399===
* '''6311''' – [[super-prime]]
* '''6317''' – balanced prime
* '''6322''' – centered heptagonal number<ref name=A069099/>
* '''6323''' – Sophie Germain prime, balanced prime, [[super-prime]]
* '''6328''' – triangular number
* '''6329''' – Sophie Germain prime
* '''6337''' - star prime
* '''6338''' - sum of the first 55 primes
* '''{{vanchor|6346}}''' – Number of verses in the [[Qur'an]] according to the sect founded by [[Rashad Khalifa]].<ref name="rashad">{{Citation|last=Gardner|first=Martin|title=The numerology of Dr. Rashad Khalifa
| magazine = Skeptical Inquirer|date=September–October 1997|url=http://findarticles.com/p/articles/mi_m2843/is_n5_v21/ai_20121071 |url-status=dead |archiveurl=https://web.archive.org/web/20040927010219/http://findarticles.com/p/articles/mi_m2843/is_n5_v21/ai_20121071 |archivedate=2004-09-27 }}</ref>
* '''6348''' – [[pentagonal pyramidal number]]<ref>{{cite OEIS|A002411|2=Pentagonal pyramidal numbers: a(n) = n^2*(n+1)/2.}}</ref>
* '''6361''' – prime of the form 2p-1, twin prime
* '''6364''' – nonagonal number<ref name=A001106/>
* '''6367''' – balanced prime
* '''6368''' – amicable number with 6232
* '''6373''' – balanced prime, sum of three and seven consecutive primes (2113 + 2129 + 2131 and 883 + 887 + 907 + 911 + 919 + 929 + 937)
* '''6397''' – sum of three consecutive primes (2129 + 2131 + 2137)
* '''6399''' – smallest integer that cannot be expressed as a sum of fewer than 279 eighth powers

===6400 to 6499===
* '''6400''' = 802
* '''6408''' – sum of the squares of the first thirteen primes
* '''6441''' – triangular number
* '''6449''' – Sophie Germain prime
* '''6466''' – [[Markov number]]<ref>{{cite OEIS|A002559|2=Markoff (or Markov) numbers: union of positive integers x, y, z satisfying x^2 + y^2 + z^2 = 3*x*y*z.}}</ref>
* '''6480''' – smallest number with exactly 50 factors
* '''6491''' – Sophie Germain prime

===6500 to 6599===
* '''6502''' – model number of the [[MOS Technology 6502]] which equipped early computers such as the Apple I and II, Commodore PET, Atari and others.
* '''6509''' – highly cototient number<ref name=A100827>{{Cite OEIS|A100827|Highly cototient numbers}}</ref>
* '''6521''' – [[Sophie Germain prime]]
* '''6542''' – number of primes <math>\leq 2^{16}</math>.<ref>{{cite OEIS|A007053|2=Number of primes <= 2^n}}</ref>
* '''6545''' – [[tetrahedral number]]<ref>{{cite OEIS|A000292|2=Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6.}}</ref>
* '''6551''' – Sophie Germain prime
* '''6555''' – triangular number
* '''6556''' – member of a [[Ruth-Aaron pair]] with 6557 (first definition)
* '''6557''' – member of a Ruth-Aaron pair with 6556 (first definition)
* '''6561''' = 812 = 94 = [[power of three|38]], [[perfect totient number]]<ref>{{cite OEIS|A082897|Perfect totient numbers}}</ref>
* '''6563''' – Sophie Germain prime
* '''6581''' – Sophie Germain prime
* '''6599''' – safe prime

===6600 to 6699===
* '''6601''' - [[Carmichael number]],<ref>{{cite OEIS|A002997|2=Carmichael numbers: composite numbers k such that a^(k-1) == 1 (mod k) for every a coprime to k.}}</ref> decagonal number,<ref name=A001107/> sum of the first 56 primes
* '''6623''' – centered heptagonal number<ref name=A069099/>
* '''6659''' – safe prime
* '''6666''' – forty-fourth nonagonal number,<ref name=A001106/> and the 11th [[Generalizations of Fibonacci numbers#Convolved Fibonacci sequences|third-convolution]] of [[Fibonacci sequence|Fibonacci number]]s.<ref>{{Cite OEIS|A001628 |Convolved Fibonacci numbers.}}</ref> In [[Christian demonology#Number|Christian demonology]] it represents the [[Christian demonology#Number|number of demons]] in a legion of demons.{{citation needed|date=August 2023}}
* '''6670''' – [[triangular number]],<ref>{{cite OEIS|A000217|2=Triangular numbers: a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 + ... + n}}</ref> [[centered nonagonal number]],<ref>{{cite OEIS|A060544|2=Centered 9-gonal (also known as nonagonal or enneagonal) numbers. Every third triangular number, starting with a(1)=1}}</ref> centered 19-gonal number,<ref>{{cite OEIS|A069132|Centered 19-gonal numbers.}}</ref>

===6700 to 6799===
* '''6719''' – safe prime, highly cototient number<ref name=A100827/>
* '''6724''' = 822
* '''6733''' - star prime
* '''6728''' – number of domino tilings of a 6×6 [[checkerboard]]
* '''6761''' – Sophie Germain prime
* '''6765''' – 20th [[Fibonacci number]]<ref>{{cite OEIS|A000045|2=Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.}}</ref>
* '''6779''' – safe prime
* '''6786''' – triangular number

===6800 to 6899===
* '''6811''' – member of a Ruth-Aaron pair with 6812 (first definition)
* '''6812''' – member of a Ruth-Aaron pair with 6811 (first definition)
* '''6827''' – safe prime
* '''6841''' - largest [[right-truncatable prime]] in base 7
* '''6842''' – number of parallelogram polyominoes with 12 cells<ref>{{cite OEIS|A006958|Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused)}}</ref>
* '''6859''' = 193
* '''6863''' – balanced prime
* '''6870''' - sum of the first 57 primes
* '''6879''' – number of planar partitions of 15<ref>{{cite OEIS|A000219|Number of planar partitions (or plane partitions) of n}}</ref>
* '''6880''' – [[vampire number]]<ref>{{cite OEIS|A014575|2=Vampire numbers (definition 2): numbers n with an even number of digits which have a factorization n = i*j where i and j have the same number of digits and the multiset of the digits of n coincides with the multiset of the digits of i and j.}}</ref>
* '''6889''' = 832, centered octagonal number<ref name=A016754/>
* '''6899''' – Sophie Germain prime, safe prime

===6900 to 6999===
* '''6903''' – triangular number
* '''6912''' – [[3-smooth]] number (28×33)
* '''6924''' – [[magic constant]] of ''n'' × ''n'' normal [[magic square]] and [[Eight queens puzzle|n-Queens Problem]] for ''n'' = 24.
* '''6929''' – highly cototient number<ref name=A100827/>
* '''6930''' – decagonal number,<ref name=A001107/> square pyramidal number<ref name=A000330/>
* '''6931''' – centered heptagonal number<ref name=A069099/>
* '''[[6969]]''' – 2015 comedic [[progressive rock]] song by the band [[Ninja Sex Party]]
* '''6975''' – nonagonal number
* '''6977''' – balanced prime
* '''6983''' – Sophie Germain prime, safe prime
* '''6997''' – 900th prime number

===Prime numbers===
There are 117 [[prime number]]s between 6000 and 7000:<ref>{{Cite OEIS|A038823|Number of primes between n*1000 and (n+1)*1000}}</ref><ref>{{cite web|last=Stein |first=William A. |author-link=William A. Stein |title=The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture |url=https://wstein.org/talks/2017-02-10-wing-rh_and_bsd/ |website=wstein.org |date=10 February 2017 |access-date=6 February 2021}}</ref>
:6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997

==See also==
* [[Year 6000]]

==References==
{{reflist}}

{{Integers|10}}

[[Category:Integers]]

6000 (number) - Revision history

>Bbb23: revert sock